Herbrand logic

[Mitchell Smith]

This post is motivated by several recent conversations -- most notably, that with Mr. Burse in which I had been reminded of a prior conversation with Mr. Greene.

Also, while I have not yet replied to Mr. Olson, he acquitted himself well with respect to the analytic conception of truth in reply to my remarks in the model theory thread. Naturally, I am not referring to the "correct reasoning" nonsense used to avoid acknowledgement that different paradigms must be respected. I did a quick Internet search on Herbrand logic to see if his use of metamathematical notation had any grounding in that logic.

But, Herbrand logic is not based upon an analytical conception of truth. One cannot make a case for his usage through that avenue.

I did, however, find an informative web page from people working at Stanford University (Mr. Greene's alma mater). Among other things, it gives explicit differences between "first-order logic" and Herbrand logic. I placed the former in quotes because there are those who would simply define "logic" in terms of syntax alone. Normaly, however, first-order logic is understood to have Tarski semantics.

The web page is at the link,

http://intrologic.stanford.edu/extras/manifesto.html

A passage within its conclusion had been of interest to me. It reads,

"To test the value of Herbrand semantics in this regard, we recently switched Stanford's introductory logic course from Tarskian semantics to Herbrand semantics. The results have been gratifying. Students get semantics right away. They do better on quizzes. And there are fewer complaints about feeling lost. It is clear that many students come away from the course feeling empowered and intent on using logic. More so than before anyway."

Aww...

Mathematics is hard. So, we should redefine mathematics so that people who are unwilling to put in the hard work can feel good about themselves.

I am more than willing to treat the study of correspondence theories of truth as an application of mathematics to philosophical problems. I have even learned to speak of "the philosophy of formal systems" in order to facilitate that perspective.

But, that is not what is going on here.

Meanwhile, physicists have put themselves into a similar quandry. Like the computer scientists, they are blaming the evil mathematicians.

The link cites some significant differences between Herbrand logic and first-order logic. By contrast, the Wikipedia page on a Herbrand structure conflates the two in its first sentence

https://en.m.wikipedia.org/wiki/Herbrand_structure

Again, this conflation is precisely why I put the first mention of "first-order logic" in scare quotes with the accompanying explanation.

God may whisper into the ear of some people; but, he does not in mine. When you all figure out how to use the word 'logic' unambiguously, I will do my best to accommodate the situation.

mitch

[Mostowski Collapse]

What do you think about "Knowledge Graphs"?

DeclarativeAI 2022 - Ivan Horcrux
https://www.youtube.com/watch?v=hWBRO8s07sE

Mitchell Smith schrieb am Mittwoch, 12. April 2023 um 14:00:16 UTC+2:
> mitch

[Ross Finlayson]

Is it a, directed, acyclic graph?

Type theory is often regular, but, intensionality and extensionality,
in the same and different, work up how exceptions are rules.

For large corpi of data, is for medium corpi of data, that have intermediate
representations the relations, reasonably as membership in classes as
sameness or "diffness" of types, is for _tractable_ forms, besides, just
sensible and then fungible forms.

This is where, a _rules_ engine is what results parallel wide over rules,
that given attributes, each typed, determine the evaluations or judgments,
of rules, for example, which rules.

So, representations, are variously variously fragments, and, variously
written in forms, that representing some kinds of relations, is well-behaved,
while representing others kinds of relations, is pathological, with respect
to the resources, time and space, which effect both evaluation of the rules,
where the parameter is part of the function or not, and, maintenance of the
rules, reflecting adaptive data structures and algorithms.

So, what about "knowledge graphs"?

[Ross Finlayson]

How about, _matroids_ or the _generalized inverses_.

In graph theory, a tree, has a representation, as a directed-acyclic-graph.

A graph, can be decomposed, to a union of trees.

A matroid, is a higher-order concept, of a matrix.

Generalized inverses, have generalized inverses, where that they are closed, is a universal algebra.

The space of values and representations, is a usual geometric concern.

In the beginning there was nothing, then there was the space.
In about the middle there's the word, words fill the space.

So, a graph in the space of graphs, is just a representation, in the space of values,
and there are values in geometry's and geometer's, and, there are values in the
algebra's and the algebraist's.

Gibberish, is named for al Geber, an Arab, who studied medicine, chemistry, and astronomy.

This is not.

[Mostowski Collapse]

Well there was another Ross, some M. Ross Quillian.
In his system you could ask:

Compare: CRY, COMFORT

And it would output:

Intersect: SAD

The example is from here:

SEMANTIC MEMORY
M. Ross Quillian - October, 1966
https://apps.dtic.mil/sti/pdfs/AD0641671.pdf

[Mostowski Collapse]

Lets see what ChatGPT gives me, 60 years after Quillian:

Q: Compare the verbs "cry" and "comfort"

A: "Cry" and "comfort" are two verbs that are
quite different in meaning and usage.

The verb "cry" refers to the act of shedding tears,
often as an expression of strong emotion such as
sadness, grief, pain, or joy. It can also be used to
describe the sound that someone makes when they
are crying. For example, "She cried when she heard
the news about her grandmother."

On the other hand, the verb "comfort" refers to the
act of providing emotional or physical support to
someone who is in distress or experiencing pain.
This can include offering words of encouragement,
a hug, or some other form of soothing. For example,
"He comforted his friend who was going through a difficult time."

While both verbs are related to emotions and can
be used in situations of distress, the main difference
is that "cry" is an expression of the person's own emotion,
while "comfort" is an action taken by someone else to
help ease the emotion of another person.

ChatGPT Mar 23 Version.

[Ross Finlayson]

What's "catharsis"?

[Ross Finlayson]

Define "homeopathic". Doesn't it assume that the reaction to a negative stimulus is a rejection,
which though after hysteresis may result a positive reaction to a negative stimulus, given that
the body has its own health?

Define "bias in the absence of bias".

[Mostowski Collapse]

Looks like the MIL link is his thesis, it says in the intro:

"The author wishes to thank all of the many people who
have graciously contributed to this thesis, providing ideas,
criticism and research funds. I am especially grateful to
my Committee Chairman, Professor Herbert A. Simon, for his
continuous support and counsel over the past three years."

SEMANTIC MEMORY
M. Ross Quillian - October, 1966
https://apps.dtic.mil/sti/pdfs/AD0641671.pdf

While Wikipedia is a little clueless:

Quillian, R. Semantic Memory. Unpublished doctoral
dissertation, Carnegie Institute of Technology, 1966.
https://en.wikipedia.org/wiki/Semantic_network

LoL

[Ross Finlayson]

Define "homeopathic". Doesn't it assume that the reaction to a negative stimulus is a rejection,
which though after hysteresis may result a positive reaction to a negative stimulus, given that

the body has its own health? It's a virial principle, in homeostasis.

Define "bias in the absence of bias".

How is "catharsis" different from "pollutance"?

So, uh, what about "Knowledge Graphs"? What kind of "Knowledge Matroid" is that?


Is yours like an Oz' little curtain behind which you can see the levers?

[Mostowski Collapse]

Your posts don't contain any words that resonate with me.
Ok, one thing I find funny: That there are two Ross. LoL

[Mostowski Collapse]

Maybe the reason that your words don't resonate, is
that they run into a void. They have no anchoring in my
brain. John R. Anderson wrote about wetware memory

models. It could increase your hit rate Rossy Boy. So
far you don't hit anything. This author, ?? Niels A. Taatgen ??,
recaps some of the models from the past in this chapter:

The architecture of cognition
https://pure.rug.nl/ws/portalfiles/portal/9884768/c2.pdf

[Ross Finlayson]

Oh, you mean "cognitive agencified thinkings" or "cats"?

Wetware shmetware, here is for "objective agencified thinkings" or "oats".

Damn I love them oats, ..., and cats.

So, back to "logical computational atoms", and a model of a computing reality,
Burse-bot you might find much gain from "pragmatic competence and its attainment
as an idealistic attainment", then above whether oats are cats and cats are oats.

You might find much gain - and squelch.

[Mostowski Collapse]

Come on Rossy Body, use your noodle, to spice
up the discussion, instead of childisch nonsense.

The next step is to come back to Tarski Semantics,
Herbrand Semantics, and see where RDF fits in.

Are triples such as:

<subject> <predicate> <object>
https://www.w3.org/TR/rdf11-primer/

Really enough?

[Ross Finlayson]

Oh, you mean OWL?

It seems you should start with "Dublin Core".

Since when have you learned the word "matroid"?

I imagine now you have a catalog of "OIDs".


You know, both "Beck" and "3 Doors Down" have, "Losers".
But, if you're a little dyslexic, it's "Lovers".
How soon we forget, ....

Heh, S-V's, ... (scalar values).

There's a great paper on the ACL Anthology that talks about
adding a time dimension to RDF, "facts".

It kinds of brings in the absolute and relative, though, ..., but,
it really makes a more modal and temporal altogether, ..., "frame".

If you've ever studied enumerated values, I imagine you know that
there are many sorts, "implicits", above "un-known" and "un-set",
that, for example, would carve out a range, for the conventional,
for example for the range, and all the projective.

It's similar with values reflecting relations in time, calendar time versus clock time.
Sometimes there's only magnitude, and sometimes there's only difference.


Anyways whatever kind of kick-me sticker you just licked,
I hope you like the taste of glue, and, it's on your forehead.
Your hallucination only contributes to halitosis.
In our schools we use non-toxic glue.


The enumerated values a set of constants and their implicit, a superset of constants,
makes for why there are simply made these simply elementary "logical computational atoms",
and it's a nice model for an analog and digital reality.

And: that there is one.

So, there's a great paper in the ACL Anthology, about adding time to RDF "facts",
and that it's rather involved the implementation.




It's like "how is thermo 1st law really different than thermo 2nd law? It's not."

You mentioned Herbert Simon, he's quoted here, ..., at 5:50.

https://www.youtube.com/watch?v=tBE06SdgzwM&t=350s

H.S. says "human level cats are around since way back".

Are words not quantities?



Now, if you'll please excuse me, I'll hope that if you're explaining Herbrand's semantics,
it includes both the internal and closed and inner, and, the context of other related semantics,
as what helps arrive at together a holistic syntax and semantics, together, then helping show
both the strengths and weaknesses, of Herbrand's semantics, given capabilities and limitations.

Such reflective contemplations or "the practice of the dialectic for the dialetheic",
can really go a long way enriching the curriculum and making better thinkers.

For less, ....


What's the easiest logic to pick up, utilize, and put down, again?
It depends on the organization, in the real world it's science,
an expert's founded nonjudgmental science.

Thusly the usual human animal spends about 1/3 of its duty cycle
in the act of sleep and dreams.


There's a recent novel called "Titan", it's about a world of ubiquitous intelligence
and variously as whether there are cats or oats, it may remind one of Frank et alia
Herbert's Dune, which begins as it ends a conversation on intelligence.

Of limited means, ....

[Mitchell Smith]

Jan,

I had been a database administrator during my information technology career.

I taught myself. Read books on operating systems, Arcnet and TCP/IP networking, database systems, general purpose programming (C) and object-oriented programming (Eiffel), and Intel desktop hardware. I also taught myself Unix in an attempt to get a first job. Made it through 3 interviews with the team supervisor, but, the "team" rejected me in the last interview. To get experience, I volunteered with a not-for-profit taking care of their computers. I learned a proprietary desktop database called Dataflex.

Dataflex had been the basis for actual employment in my first two jobs. I learned MS Access SQL at the second job as part of the product migration. With SQL, I landed a job at the National Center for Supercomputing Applications working with Sybase. That led to a job with IBM Global Services supporting nuclear power plants.Then I taught myself Oracle and foud a job with a local, regional university. I wrote an operational data store application acceppting IBM 360 mainframe data using Bourne shell, sed, and awk (who needs Perl? just more unnecessary make-a-buck technology). I never had the chance to convert it into a full-fledged C application.

Because of a break forced on me because my mother went into hospice, I had some time and took corses with Sun Microsystems. I became a certified systems administrator and network administrator. My last "good" job had been as the quality assurance DBA for the Internet application division of the Bank of Montreal running Oracle test platforms on 26 Sun Microsystems servers.

RDF had been proposed before the dot-com debacle. I had been studying all of the W3C technologies for the semantic web just before "math-believing" economists at the Federal Reserve trashed the US economy.

You are asking my opinion about a technology for which I had planned to acquire a professional expertise. I had been excited to learn all of these technologies at that time. And, I am still highly respectful of the work done in information technology. But, I don't buy into the hyperbole of its "corporate culture."

One may compare the section of the video discussing the logical problems as not being an impediment to particular problems with the fact that one can approximate solutions to high-order polynomials with numerical analysis despite the results of Galois theory. Denying mathematics which one finds objectionable does not make it go away.

Except, perhaps, when I have somtimes lost my temper, I have never been the person in this newsgroup dismissive of other people's mathematics. I find information technologies to be quite interesting. But, a person has only so much time...

mitch

[Julio Di Egidio]

On Thursday, 13 April 2023 at 03:42:00 UTC+2, Mitchell Smith wrote:
> On Wednesday, April 12, 2023 at 9:42:19 AM UTC-5, Mostowski Collapse wrote:
> > Mitchell Smith schrieb am Mittwoch, 12. April 2023 um 14:00:16 UTC+2:
>
> > What do you think about "Knowledge Graphs"?
> > DeclarativeAI 2022 - Ivan Horcrux
> > <https://www.youtube.com/watch?v=hWBRO8s07sE >
>

> Jan,
> I had been a database administrator during my information technology career.

LOL.
Your use of the past tense indeed is fucking ridiculous.

> You are asking my opinion about a technology

No, he isn't.

Come, use your noodle and get the fuck out of here,
you other complete and completely insane fraud.

Julio

[Mostowski Collapse]

You forgot some important details of your CV:

In 2022 I got hired by SBF to work for FTX. My dedication
to custumer expierence led me to choose QuickBooks from
Intuit. As a proven leader in directing operations, maintenance
and support of complex systems, I advised the customer
to mark 80'000 unprocessed transactions as "Ask My Accountant".
This did boost their brand recognition and customer
satisfaction tremendously.

https://twitter.com/SecretCFO/status/1646130148381540359

Mitchell Smith schrieb am Donnerstag, 13. April 2023 um 03:42:00 UTC+2:
> ... Internet application division of the Bank of Montreal ...
> mitch

[Mitchell Smith]

On Wednesday, April 12, 2023 at 9:42:19 AM UTC-5, Mostowski Collapse wrote:

Jan,

One thing to notice toward the end of the presentation involves "adjustments" that needed to be made. Among them is "negation as failure." I am aware of negation as failure, but could not explain it off of the top of my head because logic programming is not my principle concern. I bring it up because of the earlier reference to classical limitations.

The issue is that the modern conception of logic is pluralistic. If you change a syntactic rule, you have a different logic. One may be able to demonstrate an isomorphism or correspondence. But, such proofs need to be considered carefully since they may introduce implicit assumptions. I am still uncertain about various comparisons between Lawvere's elementary category of sets and Zermelo-Fraenkel set theory that I have read -- the analyses seem too simplistic. So, the video contains a non-trivial apples-and-oranges comparison.

They also discuss correctness proofs for algorithms. This is an important aspect of information technology which has bearing on the various claims for mathematical foundations.

In response to Goedel's incompleteness, Willard has investigated self-verifying theories. Incompleteness is related to multiplication (and addition, presumably) as a total function/operation.

Certain principles of intuitionism are compatible with this. Naturally, then, the intuitionistic origin of Martin-Lof type theory lends itself to verificationism. This is, in fact, the case. When Steve Awodey and Andrej Bauer demonstrated their childishness for all the world to see on the FOM mailing list, I followed numerous blogs discussing the controversy and downloaded reference papers. I seem to recall a paper by Martin-Lof explicitly stating this for his work, although I cannot give a reference at the moment.

So, again, while they refer to classical limitations, the practical needs of the technology introduce changes that make the comparison irrelevant.

As for the general use of graphs, my own work has led me to think of edges in terms of difference relations. I do not say this with respect to all possible uses of graphs. Rather, our intuitive notion of distinct points in space can be correlated with the line segment joining two points. This is typically understood relative to convexity and parameterized with a formula such as

p(t) = x*(1-t) + y*t, where t in [0,1]

But, this is implicitly introducing an order via the domain for t. For logical purposes, I had chosen to "represent" this situation in terms of a "there and back" path. This still requires the use of a "distinguished" point to be initial.

The syntactic form is my "discernibility relation" discussed on page 12 of the link,

https://drive.google.com/file/d/15IdSKGmmHgUcC3-TopCkE4khF4XHZwm7/view?usp=drivesdk

The formula contains no nested quantifiers. The denied relation is intended to assert singularity without asserting existence. Like a "back and forth" along a line segment, the relation is symmetric.

By contrast, consider homotopy type theory.

Eilenberg and Maclane developed category theory in order to "ground" their idea of a natural transformation. To a large extent, it is backwards engineered to recreate previous notions of algebraic foundations. Maclane briefly confirms this with a remark in "Categories for the Working Mathematician."

The general notion of an arrow in category theory comes from continuous maps in algebraic topology. This continuity assumption masks the kind of exceptions which must be dealt with in vlassical calculus (essential and removable discontinuities). What is, in fact, the case is that two functions f(x) and g(x) are homotopy equivalent if f(x) and g(x) can be joined by a line segment for every x in the domain.

Consequently, where I have taken line segments as a basis for understanding differences, alternate views assume them as a basis for sameness.

Indeed, the gif at the link

https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/10/Category_Theory-fig3.gif

is from a Quanta article making "great claims" about all of mathematics,

https://www.quantamagazine.org/with-category-theory-mathematics-escapes-from-equality-20191010/


I am not an asshole "just because." People in fields that I once respected have destroyed their own credibility by behaving like narcissistic pricks.

mitch

[Mostowski Collapse]

You are barking the wrong tree. You make RDF a non-classical
versus classical logic case. Why would one present "knowledge graphs"
from this angel and contrast it with category theory etc..?

This doesn't make any sense. Lets say category theory is simplified
about boxes and arrows plus some extra structure. Guess what you
get if you put these building blocks together:

> Are triples such as:
> <subject> <predicate> <object>
> https://www.w3.org/TR/rdf11-primer/
> Really enough?

Why give these triples so called "knowledge graphs"? Any clue? So
far Ross Finalyson was clueless. How about Mitchell Smith, is he also
totally clueless? BTW: Here is a small example of tripples:

<Bob> <is interested in> <the Mona Lisa>.
<the Mona Lisa> <was created by> <Leonardo da Vinci>.

And here as a knowledge graph:

. Bob --- is interested in -- the Mona Lisa
. |
. was created by
. |
. Leonardo da Vinci

See also:

Is Category Theory similar to Graph Theory?
https://math.stackexchange.com/q/1239027

Mitchell Smith schrieb am Donnerstag, 13. April 2023 um 14:02:19 UTC+2:
> ... Eilenberg and Maclane developed category theory
> in order to "ground" their idea of a natural transformation. ...
> mitch

[Mostowski Collapse]

Dang Google groups tends to remove spaces,
so I replace spaces by period. Should show like this:

<Bob> <is interested in> <the Mona Lisa>.
<the Mona Lisa> <was created by> <Leonardo da Vinci>.

And here as a knowledge graph:

. Bob --- is interested in -- the Mona Lisa

. . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . . . . . . . . . . . . . . . . was created by
. . . . . . . . . . . . . . . . . . . . . . . . . . . . |
. . . . . . . . . . . . . . . . . . . . . . Leonardo da Vinci

[Mostowski Collapse]

My suspicision, Mitchell Smith is a payed troll,
trying to lure people into his snake-oil cave?

Like the carpet seller in Antalya that offers a little
tea, before trying to incarcerate his victim, until

it buys some bullshit. LoL

[Ross Finlayson]

Perhaps you'd find more bodies of fact if you learn
some COBOL and various record formats of the EDI,
though then you'd probably get interested in packet formats
other than the old Address Family Inet and Unix, and
more-than-less start wondering what's up on the old main-frame.

But, maybe just some knowledge of Dublin Core and RegAut
will get your Riegenstrief steps up to count.


The KIF and Knowledge Interchange Format rather predates it.

Mostly though our knowledge though is contained in what's
called "the stacks".

[Ross Finlayson]

There are at least two kinds of paranoia:
1) they're out to get you
2) you're out to get them
and at least two usual responses to hysteria,
1) recoil
2) scapegoat
and at least two usual responses to suspicion,
1) suspicion gets raised,
2) suspicion gets raised.

But, this is where, that's the role of a: suspician.

Here we're happy skeptics not pinched cynics,
and not "suspicians" of the usual sorts.

But, if you think someone scorned has a fury,
a pinched cynic is the sort to get revenge.

[Ross Finlayson]

I'm glad that you separate homotopy and types from "homotopy types", and point
out that what's categorical because homotopy models it doesn't just automatically
fix un-categorical type theory. It's like "sun worshippers" of a sort, "it made me blind,
I must've seen".

About Quanta Magazine, on the one hand, the articles often sound great, but, pretty
much, at some point they'll describe an interesting enough new researcher in an old field
unawares of the surrounds or context, make a wildly unscientific or unmathematical claim,
then turn to a different scientific or mathematical claim as off it, then it results mostly
they're for reading as for templating it to those kinds of parts, i.e., reading for awareness,
of their errors, not reading for uncritical consumption, as what's undigestable.


There are lots of theories: sets and parts, categories and types, ramified and stratified types,
theories with only the predicative, theories with transfer principles about the impredicative,
arithmetics and all sorts algebras, number theory and machine number theory, geometry,
function theory, operator theory, dynamical modeling, and all sorts analysis of any calculi,
there are lots of theories.

Yet, some people never even deconstruct arithmetic where addition is a thing, and, division
is another thing, and, they make a meeting in the middle like the complete ordered field.

Some people never even deconstruct the Cartesian and coordinates, for that matter every
single diagram and formula they've ever seen is framed in it.

The challenges of _putting the theories together_, is quite a thing, where, first off, the theory
of real numbers, still has the examples of Jordan measure ("not a measure / no sigma algebras,
Aristotle's continuum, path or line element of a path or line integral, iota-values"), or the Dirichlet
function ("rationals 1 irrationals 0, dense everywhere continuous nowhere, but its complement
is a union and continuous"), with the good-old complete ordered field, has that _in extremis_,
the "metrizing ultrafilter" or about the "pesudo-differential", _makes those things_, what are
_models of those things only in their own theory models of those things_, what are though
CONTRADICTORY to EXIST as next to the other primitives in the theory ("in the limit and at
the limit".)

So, it makes for a deconstruction of limit theory, for, ..., continuity theory, where the limit exists
and how to make it from unfettered induction, and, where the limit is the sum, and how to make
it that there's some "complete induction" that results like the transfer principle as "what's so for
each individually is so for all as an individual or whole".

[Mostowski Collapse]

Troll alert.

Ross Finlayson schrieb am Donnerstag, 13. April 2023 um 20:50:31 UTC+2:
> .. herpes blister gibberish ...

[Mostowski Collapse]

Anyway, its not my problem if Ross Finlayson pollutes the
thread of Mitchell Smith, or should I call him Mr. Smith.
You, Ross Finlayson must then be Ms. Smith?

It would also never come to my mind to title a thread
"Herbrand Logic". Thats just cock gobbling nonsens.
And an internet search will yield nothing, thats just a

balant lie. The choice of the title indicates that the OP
of the thread has little to no clue about Herbrands theorem,
or who even Jacques Herbrand (1908 – 1931) was.

LMAO!

Mitchell Smith schrieb am Mittwoch, 12. April 2023 um 14:00:16 UTC+2:

> This post is motivated by several recent conversations -- most notably, that with Mr. Burse in which I had been reminded of a prior conversation with Mr. Greene.
>
> Also, while I have not yet replied to Mr. Olson, he acquitted himself well with respect to the analytic conception of truth in reply to my remarks in the model theory thread. Naturally, I am not referring to the "correct reasoning" nonsense used to avoid acknowledgement that different paradigms must be respected. I did a quick Internet search on Herbrand logic to see if his use of metamathematical notation had any grounding in that logic.
>
> But, Herbrand logic is not based upon an analytical conception of truth. One cannot make a case for his usage through that avenue.
>
> I did, however, find an informative web page from people working at Stanford University (Mr. Greene's alma mater). Among other things, it gives explicit differences between "first-order logic" and Herbrand logic. I placed the former in quotes because there are those who would simply define "logic" in terms of syntax alone. Normaly, however, first-order logic is understood to have Tarski semantics.
>
> The web page is at the link,
>
> http://intrologic.stanford.edu/extras/manifesto.html
>
> A passage within its conclusion had been of interest to me. It reads,
>
> "To test the value of Herbrand semantics in this regard, we recently switched Stanford's introductory logic course from Tarskian semantics to Herbrand semantics. The results have been gratifying. Students get semantics right away. They do better on quizzes. And there are fewer complaints about feeling lost. It is clear that many students come away from the course feeling empowered and intent on using logic. More so than before anyway."
>
> Aww...
>
> Mathematics is hard. So, we should redefine mathematics so that people who are unwilling to put in the hard work can feel good about themselves.
>
> I am more than willing to treat the study of correspondence theories of truth as an application of mathematics to philosophical problems. I have even learned to speak of "the philosophy of formal systems" in order to facilitate that perspective.
>
> But, that is not what is going on here.
>
> Meanwhile, physicists have put themselves into a similar quandry. Like the computer scientists, they are blaming the evil mathematicians.
>
> The link cites some significant differences between Herbrand logic and first-order logic. By contrast, the Wikipedia page on a Herbrand structure conflates the two in its first sentence
>
> https://en.m.wikipedia.org/wiki/Herbrand_structure
>
> Again, this conflation is precisely why I put the first mention of "first-order logic" in scare quotes with the accompanying explanation.
>
> God may whisper into the ear of some people; but, he does not in mine. When you all figure out how to use the word 'logic' unambiguously, I will do my best to accommodate the situation.
>
> mitch

[Ross Finlayson]

PostScript: the Burse-boy's "Lols", are not so droll, as it rolls its trolls, so hold your nose,
ignore its pose, though everyone likes a good laugh every now and then, it's not one.

Those poor Burse-bots, ..., "my wetware master poked us all, and my joke a poke was the
only one that hid his chagrin from his hypocritical sin, Lol, they're all dead."


Some few times I've applied psychology to it, the "Burse-bot in the Burse-box",
it causes a lot of wetware mucking the boxes because often they'll gain a bit
of conscience, so Burse has installed "nonsense rules" largely.



It's kind of like, my, "model of an inner angry black man", he's a member of my inner
"80 man black caucus". Every day, the caucus debates issues, then after lunch, 40 of
them have heart attacks and are ceremonially rolled out, and 40 new ones sworn in.

But, you know, they're volunteers.

[Mostowski Collapse]

The point of Herbrands theorem is to show that there is
no difference in Tarski semantics and Herbrand domain
semantics for first order logic, Jacques Herbrand

even devises a proof method, based on this insight,
which is one of the most successful proof methods and
now used in almost all theorem provers, in the form

of for example unification. Hebrands informal account [1930]
seems to be similar to what later became the transformation
based algorithm by Martelli and Montanari [1982]:

> A unification algorithm was first discovered by Jacques Herbrand,
> https://en.wikipedia.org/wiki/Unification_%28computer_science%29

There are some extensions of Herbrand and/or Unification
to other Logics. Its not confined to either classical logic, can
also be the basis for non-classical logics, and it is not confined

to first order logic, there are also extensions to higher order logic.
Even Coq uses unification, you can try yourself:

Coq < Lemma ex: forall (P:Prop), (P -> False) -> P.
Error: In environment
intros P, J
apply J.
Error: In environment
P : Prop
J : P -> False
Unable to unify "False" with "H".

Ross Finlayson schrieb am Donnerstag, 13. April 2023 um 21:54:13 UTC+2:
> ... more nonsense on the run ...

[Mostowski Collapse]

Credits for this finding about Coq, go to Julio Di Egidio.
A nice example of a participant that is not an anaemic troll.
How do you trolls, like Ross Finlayson or Mitchell Smith,

even go into the sunlight or close to garlic? You
will die if you cannot suck the blood of sci.logic
participants by posting mamut scrolls of utter nonsense.

[Mostowski Collapse]

Credits to move my lazy ass, and investigate a little
bit what Coq is doing, especially "apply" and "intros".
So this was also one spin off from these investigations.

And they show also why my validate/4 prototype works.
This page from Coq contains 6 mentions of unification. It seems
Coq combines unification with constraint solving.

https://coq.inria.fr/refman/proofs/writing-proofs/proof-mode.html

This is a reasonable approach in some higher order logic
settings. But maybe they use it also for other purposes.
Don't know exactly what they are doing.

Also I don't know how deep Julio Di Egidio has already
put his nose into the unification part of Coq?

[Ross Finlayson]

How does it read Leibniz' monadology? Is it not monadic?

The "unification" you reference is only "closures".
Here there's also "open unification".

It's nice though that this "unification" effort at least models
the "inverting the diamond" as it were, but, it's still bereft what
is some "original analysis".

It seems you describe there an infinite _space_ of the language
of 0's and 1's that include all infinite sequences of 0's and 1's, ....

It might be all 0's and 1's down there, and all 0's and 1's up there,
then that it's all true and false in here, what's all true.

It's nice though to have an overall model of embeddings and extensions
what result for intensionality and extensionality an operator calculus,
must be nice.

It's all so though plainly digital, what that it appears to be
your "the logic", there.

A great thing about Cantor space, is that, first of all is that its a space.
Another great thing about it is that in the Cartesian, it's infinitely long.
Another great thing about it is that in the Aristotlean, it's square.

Then, what's "line-drawing an anti-diagonal" in the one
is "line-drawing the diagonal" in the other,
one algebraic in words, the other geometric in a space.

This sort of, "unification", where what you've linked there might simply
be called "generalized inversion in regular types", is a pretty great thing.

The, "unification", though, there's already quite a body of desiderata and
requirements of such "one theory with the works", that what you've got
there is "exercises in extensionality in type theory".

At best Incomplete, ..., Goedel's, ....

Otherwise it's great though "applications of reflections in inverses
the generalized for loose model theory".

[Mostowski Collapse]

Well this reminds me again of my philsophy teacher,
who though he can cope with modern logic by tweaking
Aristoteles Barbara. Otherwise he was mumbling

something about Gödel, but most of all he was happy
to soon receive his retirement notice. Or in short:
FUD, from a batshit crazy idiot named Ross Finlayson.

https://en.wikipedia.org/wiki/Fear,_uncertainty,_and_doubt

[Mostowski Collapse]

Anyway, I wouldn't care less about this thread, that
I neither own and neither endorse. I would never title
a thread "Hebrand Logic", it simply doesn't make any sense.

But I had my fun, horsing around a little bit with RDF,
and seeing what the Echo is. The Echo was actually Zero.
I don't expect anything sensible about Unification flowing in,

the thread was already written off at its beginning.
It was already discounted to zero in its value rigjht
from the start 12.04.2023, 14:00:16. Just re-read

the main post, it contains quite a quantum of nonsense.

Mostowski Collapse schrieb:

[Mostowski Collapse]

I didn't know this paper:

HERBRAND' S FUNDAMENTAL THEOREM AND
THE BEGINNING OF LOGIC PROGRAMMING
FRANCINE ABELES
https://projecteuclid.org/journalArticle/Download?urlid=rml%2F1204835163

[Ross Finlayson]

"I can't do nothing for you, man."

It's like the integers, and old Kronecker,
"G-d gave Man the integers, all the rest is the work of Man",
and it's like, "to hell with you, Kronecker,
the integers are as emergent as anything else,
and mathematics is discovered, not invented."

[Julio Di Egidio]

On Thursday, 13 April 2023 at 23:51:23 UTC+2, Ross Finlayson wrote:

> "I can't do nothing for you, man."

Apart from sucking innocent blood
while polluting every pond, you always
self-apologetic piece of insane nazi-shit
with a view.

ESAD.

Julio

[Ross Finlayson]

Don't ..., don't, don't, don't:
Don't believe the hype.


There's some theories that Struick an historian is quite old.


Furthermore, I am _not_ a "socialist progressive".
It's like today, I picked up a copy of Polybius, and
I'm reading about how Hannibal corraled and defeated Flaminius,
then that he gets into the strength of the Roman Constitution,
where for example Augustine is a devoutly professed Platonist.

Furthermore: not sorry, not sorry.

Thanks, I already had my blood.

About Herbrand and "free logic", "universal logic",
I'm a simple computer programmer.

Yeah, yeah, I know, "Carthago delenda est".


Anyways now that it's more clear that Mitch's reference to Herbrand
is the touchstone of these "unificationalists the digital in loose
types in strong types", as it were, then I'm glad that I already have
an analysis and a synthesis of a geometry the analog, an analog.

It's a continuum mechanics.

[Julio Di Egidio]

On Friday, 14 April 2023 at 01:00:54 UTC+2, Ross Finlayson wrote:

> About Herbrand and "free logic", "universal logic",
> I'm a simple computer programmer.
> Yeah, yeah, I know, "Carthago delenda est".

You blood-sucking self-apologetic piece of
fraudulent nazi-shit with a view don't know
anything at all.

Julio

[Mostowski Collapse]

Hi,

You sure you are dreaming of Cats? Maybe they are
yellow Caterpillars instead? Or Apache Helicopters?

https://en.wikipedia.org/wiki/Caterpillar_Inc.

Bye

Ross Finlayson schrieb am Mittwoch, 12. April 2023 um 22:27:36 UTC+2:
> Oh, you mean "cognitive agencified thinkings" or "cats"?

[Ross Finlayson]

Like the D-6 or the AH-64? What about the brush blade and Comanche?

(I'm familiar with the operation and the bill-of-materials,
the engineering bill-of-materials, the process bill-of-materials,
the manufacturing bill-of-materials, about parts and assemblies
and parts in carts and dock to stock, control stations and control points,
the jig, the big bone, the end items, parts and assemblies,
less like T-1000 and more like S1000D, parts and programs,
parts with names and parts with just, ..., numbers, SQL and the main-frame.
An engineer is a legendary creature that turns charcoal and tree pulp
into flying machines.)

It's like a stack of folios a half-mile high.

It's like "AP's the brains of a dishwasher, have you seen Lawnmower Man?
It's after Flowers for Algernon, and reflects why foundations, sole and small,
means that accelerating stupid with a bank of GPUs just multiplies the stupid".

No, I dream a lot about a lot of cats, though. And I love them oats.

Here then those are a usual man's cats and oats, that "CATs and OATs"
reflect "follow the red dot point to how bad the pain is" versus,
"it thinks, ..., like a man".

"How low, can you go?"

The "unificationalist" mentioned goes a long way toward a monotone,
modal, temporal logic, a lot longer way, than your usual "quick, broken, poofs".

Anyways the "geometric metamathematics" is more what's going
on about an "analog reality" than yon "digital twins".

[Mostowski Collapse]

The Donkey Anaphora gets especially simple in Prolog:

own(donald, sugar).
beat(X,Y) :- own(X,Y).

?- beat(donald, sugar).
true.

As a bonus Prolog can also compute an answer substitution:

?- beat(X, Y).
X = donald,
Y = sugar.

Can Coq do the same?

[Julio Di Egidio]

On Saturday, 15 April 2023 at 08:42:36 UTC+2, Mostowski Collapse wrote:

> The Donkey Anaphora gets especially simple in Prolog:
>
> own(donald, sugar).
> beat(X,Y) :- own(X,Y).
> ?- beat(donald, sugar).
> true.

EVERY Donald who owns ANY Sugar beats THAT Sugar.
In other words, yours is NOT the Donkey anaphora, it is
at best a simplification and with the property that it
totally misses the very point of the "paradox", which
is a point about *relative pronouns and clauses*.

Julio

[Julio Di Egidio]

To be more concrete:

`beat(X,Y) :- own(X,Y).`

That is the *axiom*
[forall x y, own x y -> beat x y].
Call it [Axy].

Keep also in mind that that is the
*intermediate and wrong* version of
the Donkey Anaphora, x and y aren't
just "anything" in the original.

Then:

```
own(donald, sugar).
?- beat(donald, sugar).
true.
```

That is the *theorem*
[own d s -> beat d s],
or [own d s |- beat d s].

and this is (the scheme of) the proof:
[own d s -> Axy d s -> beat d s],
which recovers Prolog's search, and

which, after unfolding, we can see
is simply yet another application
of Modus Ponens, i.e. the theorem
has the form ([A->B,A|-B]), where
[A->B] is the form of our axiom.

Julio

[Mostowski Collapse]

Thats rather silly to read the auxiliary predicates farmer x and
donkey y or some types Farmer or Donkey into the Donkey Anaphore.
Its a problem from intensional logic and Montague grammars,

how to assemble such a sentences as the Donkey Anaphore. The
paper that introduced the problem in another thread to sci.logic
was this paper, a reference you sweept under the rug:

Donkey Anaphora: Type-Theoretic Semantics
with Both Strong and Weak Sums
Zhaohui Luo - 10. November 2022
https://aclanthology.org/2021.cstfrs-1.5.pdf

The intensional logic/Montague grammars problem is found
on page 46, formula (3).

(1) Every farmer who owns a donkey beats it.
(3) ∀x. [farmer(x) & ∃y.(donkey(y) & own(x, y))] ⇒ beat(x, y)

You see better what goes wrong in the above assembling,
if you use own' instead own:

(1) Every farmer who owns a donkey beats it.
(3) ∀x. ∃y.own'(x, y) ⇒ beat(x, y)

You get a free variable y, the scope gets wrong. So linguistically
the "it" moved out of a quantifier scope, during the translation
into logic. Whereby its quite irrelevant whether its Coq or FOL.

Thats the problem of the Donkey Anaphora, the Anaphore,
the particle "it".

[Mostowski Collapse]

To be closer to Coq, I guess the problem needs to be stated as
follows, since these proof assitants have strange forall
syntax and binding priority. So the sentence that goes wrong:

The author of the paper characterizes the problem as,
I placed overly careful parenthesis, now otherwise one might
think that the variable x has also lost its scope:

(1) Every farmer who owns a donkey beats it.

(3) ∀x. ((∃y.own'(x, y)) ⇒ beat(x, y))

"For example, in a traditional compositional semantics, the
donkey sentence (1) would obtain (3) as its interpretation,
which is not a well-formed formula since the variable y in
beat(x, y) is out of the scope of the existential quantifier."

Donkey Anaphora: Type-Theoretic Semantics
with Both Strong and Weak Sums
Zhaohui Luo - 10. November 2022
https://aclanthology.org/2021.cstfrs-1.5.pdf

[Mostowski Collapse]

I little puzzle. Why does Coq have two product types?

As a proof term: fun x : A => B
As a type: forall x : A, B
https://coq.inria.fr/refman/language/core/assumptions.html

Is this really needed?

[Mostowski Collapse]

Maybe Coq doesn't have a sum type. Lets say sum types
are something like a record type, making tuples and stuff.
One can do this in lambda calculus as follows:

pair=λa.λb.λf.((f a) b)
first=λp.(p λa.λb.a)
second=λp.(p λa.λb.b)
https://sookocheff.com/post/fp/representing-pairs-and-lists-in-lambda-calculus/

So if we were to use sum types for existential quantifier
which has always a witness, we could just use a pair
as a proof term, allowing to extract a witness and a proof:

G |- s: A(t)
----------------
G |- <t,s>: ∃xA(x)

Isn't this essentially what Agda does?

∃ {A} B = Σ A B
syntax ∃-syntax (λ x → B) = ∃[ x ] B
https://plfa.github.io/Quantifiers/#existentials

[Khong Dong]

On Wednesday, 12 April 2023 at 06:00:16 UTC-6, Mitchell Smith wrote:

> Meanwhile, physicists have put themselves into a similar quandry. Like the computer scientists, they are blaming the evil mathematicians.
>
> The link cites some significant differences between Herbrand logic and first-order logic. By contrast, the Wikipedia page on a Herbrand structure conflates the two in its first sentence
>
> https://en.m.wikipedia.org/wiki/Herbrand_structure
>
> Again, this conflation is precisely why I put the first mention of "first-order logic" in scare quotes with the accompanying explanation.
>
> God may whisper into the ear of some people; but, he does not in mine.

> When you all figure out how to use the word 'logic' unambiguously, I will do my best to accommodate the situation.

"Mathematics is the mortal introspection about own knowledge inference — via symbols in particular." -- https://qr.ae/prNPiu

If you care/could, please "accommodate the situation". Thanks.

> mitch

[Mitchell Smith]

Hi Nam. I hope you are doing well.

What I believe about mathematics certainly involves our own mortality. I do not concern myself over infinities and circularities. Whatever may be the case with respect to their objective existence, they seem necessary to our explanations. For that reason, I associate them with our subjective experience.

I do not believe mathematics to be a purely linguistic phenomenon. But, our capacity to reduce our representations to binary representations opens up the idea that the subjective experience of left and right is the fundamental experiential invariant upon which to understand "foundations."

Our language is replete with dichotomies and binary oppositions.When we reduce mathematics to logic, we embark upon linguistic analyses. Russell had eventually written a paper asking if mathematics is purely linguistic. Logic certainly involves reductions based upon lingustic usage.

I will not be posting for long. I had hoped that someone might choose to look at my inference rules and derivations and give me feedback. This is not the forum for such a thing. But, I have no educated family or colleagues. So, I had to try.

In the thread on a geometric metamathematics, I posted a link to a research note,

https://drive.google.com/file/d/15087p1Io6K8xOZO2NUFzv_m7UAks1rTq/view?usp=drivesdk

I would not expect anyone to read it in its entirety. You might find the introductory remarks of the first few pages interesting. It is an attempt to motivate the "associations" whose syntactic details are collated in the appendixes.

For what this is worth, all I have learned over the last 20 years since first posting on these newsgroups is that no one can fill in the blank,

"Mathematics is ...."

Certainly not me.

mitch

[Ross Finlayson]

Thre's mathesis and poesis, whether geometric metaphor or lyrical metaphor,
that there's a strong metonymy is for a time and place or name and meaning,
and about how they're both the same.

I found a later book of Russell the other day and it's all about "power".
So, where I already have Russell as a hypocrite because of his "1+1=2,
Principia Mathematica" and "ha Frege, we stole your ball and put it in a cage",
Russell on power seems along the lines of "you don't nuke me, I nuke you".
But, maybe it's mostly that his hypocrisy about well-foundedness of the
same infinite he made Frege cry about, is why it's like "to hell with you
old Kronecker, the integers are emergent as anything else" then for
"why, there isn't a standard model, of integers, at all, it's non-standard".

It's still all complete and consistent and so on, ultimately, and all the same
useful mathematics arises, and more to boot, I was talking to a Rhodes Scholar
the other day, and he told me about mathesis, where he learned about it in
a Cambridge office, that it's going through the motions, didactic geometry.

Geometry is motion.

"Is" is.

[Ross Finlayson]

Oh, those there are, uh, "unbounded lattices", these are, "infinite lattices".

Also each lattice point is a free basis and a singular origin.

That "lattice, ordering's" seems "operator adapters for algebra",
here it's "lattices live on a continuous manifold".

They each attain to each other, of course.

[Mitchell Smith]

Try, "witnessable space is dynamic."

So, although useful, time as an algebraic dimension is unwitnessable.

I have been thinking a great deal about aperiodic tilings as a mathematical proxy for witnessing a dynamic continuum. Relative to "arithmetization," the best work I have found is that of Kari and Culik.
For 3-space, they have the paper,

https://www.semanticscholar.org/paper/An-Aperiodic-Set-of-Wang-Cubes-Cul%C3%ADk-Kari/0160bfae2af53a2f3df4f82aa0ab4b57ac331db8

It is behind a paywall, unfortunately. But, numerologically, I find the 21-set interesting.

When I first realized that "negation," "conjugation," and "contraposition" could be understood as collineations in a geometry, the 21-point projective plane became a focus of my thoughts,

https://drive.google.com/file/d/1J4udRS-mWiT__ia4PnBU80gxdqPt4aeV/view?usp=drivesdk


If any links fail to open, let me know.

mitch

[Mostowski Collapse]

Whats the trick behind this logic:

"In 2015 Dag Prawitz (see [3]) proposed an ecumenical system,
a codification where classical logic and the intuitionistic logi
could coexist “in peace”. The main idea behind this codification
is that the classical and the intuitionist share the constants
for conjunction, negation and the universal quantifier, but each
has her/his own disjunction, implication and existential quantifier"
https://philomatica.org/wp-content/uploads/2019/10/Proof-Theoretic-Semantics-2019.pdf

Thats a little bit against my mainstream thinking, where one
thinks about two different negations as well. Does this
mean the common negation is the intuitionistic one?

How does the calculus wangle negation? Could find the
Dag Prawitz paper as a PDF yet. But this might shed some
light on the question, although had only time to gloss it:

Ecumenical modal logic
Sonia Marin, Luiz Carlos Pereira, Elaine Pimentel, Emerson Sales
Submitted on 28 May 2020
https://arxiv.org/abs/2005.14325

[Ross Finlayson]

Think of it this way,
it's like a poll, where nobody shows up.

No?

Then the poll comes in and everybody goes
"that poll is bullshit, I'll never believe that pollster again".

It's like, every poll, always includes the question,
"do you take this poll", and, if they added all
the same that said, "no", most would be
"don't know, or don't care, or don't ask".

It's like 95+% of polls would be 95+% "no response",
not, "response is no".

Different negations, ....

Now, remember, squeaky wheel gets the grease.
Which is funny because the nailhead that sticks out gets hammered.


Anyways, the "transfer principle" can be pretty strong,
and help reflect for example in this theory, we have two
models, and, they're not compatible, because, their structure
witness what would be breaks, but, they also share some
joint bridge results, that according to transfer principle,
model a third space of values, where, the relations in values,
can be seen to hold, relating structural features.

So, such an "ecumenical model-theoretic model-modeling
proof milieu of otherwise independent and contradictory
model-theoretic proof-theoretic truth-tableau" can relate
results of otherwise incompatible models in for example,
sets or ordinary sets, for example resulting "what's available
as bridge results, allow quantificationand conjunction this
way", _above_ the otherwise "independent models", having
basically stratified out their types.

This is pretty simple for example if you think of it as "hiding
memory locations and equating values through an accessor
and a mutex", when for example comparing and contrasting
floats and ints.

Which is pretty usual, ....

[Mostowski Collapse]

What does the phrase "which is pretty usual, ..." mean?
That a herpes blister just burst in your face Rossy Boy?

[Ross Finlayson]

Nope, it means "applications in extensionality", you freak.

(Was: "No, thanks, one of my wives already beat me today. Thoroughly.")

I don't know why, but the only time I have to worry
about "herpes" is when it's coming out of Burse's mouth,
so, ..., I suppose that's one of his greatest shames.
Or, maybe it's familiar and intimative in his queer culture -
that its shamanic tradition of tongue-lolling finds its
greatest height when he's painted himself half-blue
and drank a bowl of chechua, waving some fetishes,
daring us all to be so tongue-lolling gay.

Until he passes out, ....



Now I hope my more gentle readers will have enjoyed this,
I write for pleasure and mostly read it that way, also.

But really it's about that the "model-modeling-milieu",
is pretty usual. Most people would call it "common" sense.

[Ross Finlayson]

Hey that conference proceedings is pretty interesting.


Once I was interested in Lof but now read more from Piazza about Makinson.

I've read about half of these abstracts now, about half are interesting.

I rather have that constructivists and intuitionists are each others'
intuitionists and constructivists, not that classicists are non-constructive
nor that intuitionists are constructivists.

Then, though, I restrict from the classical some common ambiguities.
I.e. it's not really free to not be constructivist.

I imagine they'll have about as much success as Nelson did.

I don't separate the proof-theoretic and model-theoretic, it's called "theory".

I like the usual ideas of conditional sequents, for, where they remove ambiguity
and don't introduce it.

Now I was most interested in this "Geometric Rules in Infinitary Logic", by the title.

It is nice to see that "natural deduction" is quite in style.

I equate the reductionist approach to the question words reflection approach,
but the idea of the question words reflection approach is about construction
of the tractable fields, via the development of various data structures in what
answers what, that makes the massively parallel in optical models natural in
the read-out of results above resources in space at time.

There's talk about the intesionality in the proof-theoretic, which is about
the same as it would be the model-theoretic, or "pure theory",
because extensionality's non-logical and all.

"Applying a Linear Logic Perspective to Arithmetic" sounds useful.

The "Paradoxical Languages" abstract is pretty good, here about the "double-point"
discussion. It's kind of like there's a wind of stroke to the left and wind of stroke to
the right, that the eliminative and introductory naturally get sheaved together in
the middle, where the wind-wall then separates the chaff.

I like this "Categorical Negation" abstract.


I like how is described "styles" of connectives, with respect to those being features.
I.e. it's better than "generic" connectives, in a sense where logic flows are natural.

Several of the papers involve inferences as systems, above statements.

Harmony sounds good, but, harmony is at least two sounds.

There's something to be said for giving alternatives equal resources in the
usual notion of that by the time alternatives exist, they're fair.

Now I'm interested in Kreisel's Brouwer's "Creating Subject".

("What's class/set distinction in homotopy type theory? It's called homotopy type theory.")
("... and infinitary disjunctions ...")


I like that somebody introduced "metapredicativity".


Then it's for that geometrizations follow arithmetizations for model theory
what result tractable milieu in values in linear and geometric approaches to
logic and stroke.




Don't get me wrong, Burse is still a freak, but he does dig up some good bones.

[Ross Finlayson]

I'm rather for the illative or univalent, because it automatically
with the infinite beyond pair-wise conjunctions makes iota-values proper -
tacking it atop standard theory doesn't do, though, for what's "extra-ordinary".

[Mostowski Collapse]

Was this already Japanese?

Ross Finlayson schrieb am Samstag, 22. April 2023 um 08:11:25 UTC+2:
> ... gibberish ...

[Mostowski Collapse]

Thats why you are a complete moron:

> I don't separate the proof-theoretic and model-theoretic, it's called "theory".

Did you learn logic on a cow farm, just like John Gabriel who
learned his stuff in an africans village? A proof and a counter model
use totally different devices, to obtain a judgement.

Never heard of Tarskis Definition of Truth and its T-Schema:

A sentence of the form "A and B" is true if and only if A is true and B is true
A sentence of the form "A or B" is true if and only if A is true or B is true
A sentence of the form "if A then B" is true if and only if A is false or B is true; see material implication.
A sentence of the form "not A" is true if and only if A is false
A sentence of the form "for all x, A(x)" is true if and only if, for every possible value of x, A(x) is true.
A sentence of the form "for some x, A(x)" is true if and only if, for some possible value of x, A(x) is true.
https://en.wikipedia.org/wiki/T-schema

Here you go, you have model theory in a nutshell. Quite different
from proof theory, isn't it? Well whats proof theory then? Can you explain
Herpes Boy? Right? Mostlikely, since you are a complete moron,

you have no clue whats in here, what the OP posted:

Mitchell Smith schrieb am Mittwoch, 12. April 2023 um 14:00:16 UTC+2:
> http://intrologic.stanford.edu/extras/manifesto.html
https://groups.google.com/g/sci.logic/c/wt-pacBrN1Q/m/qA4DfiF7BAAJ

Why do you even post on sci.logic, if you are clueless like a
headless chicken? Is it the brain Herpes? Why are you
attention whoring if you are totally clueless?

Your nonsense is nothing else than blistering crazy spam!

[Mostowski Collapse]

You are a liar. You didn't post some inference rules and derivations
in this thread. Maybe post your crying in the relevant thread where
you posted some inference rules and derivations.

Also you are confusing some pragmatics of logic. Herbrands
theorem has a model theoretic and a proof theoretic aspect.
In 1918 when Wittgenstein wrote the Tractatus, how far was

model theory and proof theory developped? Was there even
Tarskis paper already? I mean who would write arcane
worshiping of Gods as the following passage, nowadays?

German Original:
Der verneinende Satz bestimmt einen logischen Ort mit
Hilfe des logischen Ortes des verneinten Satzes, indem er
jenen ausserhalb diesem liegend beschreibt.

English Translation:
“The denying proposition determines a logical place,
with the help of the logical place of the proposition
denied, by saying that it lies outside the latter place."
https://www.wittgensteinproject.org/w/index.php/Logisch-philosophische_Abhandlung#4.0641

LoL

[Mostowski Collapse]

Conclusion, Mitchell Smith is indeed a payed troll,
whereas Rossy Boy is just a clueless moron.

[Ross Finlayson]

No, no, no, Burse, you're doing it all wrong - when you want to make someone
out to be a parody you must someone convince them to take the bit - it only
works when they end up in a humane condition knowing they took the bit -
not a frothing lunatic such as you portray as you loll, which is only pathetic.

It's like, "the Knights, who say Ni", and that one who keeps trying and
going "Nu!, Nu!", and can't quite seem to get and carry the point.
Burse, is, a cargo cult fanatic, and pretty much is a boat of
"WM, JB, and JG: one big nut".


Then about these conference proceedings again I enjoyed Piazza's
outline and Negri's outline and various of the forms in inference and
all sorts what results models of connectives what make use proofs in
"proof-theory model-theory", where, I'm still looking for otherwise
like in the "ecumenical" example that there are quantifiers disambiguated
because usual pluralization is an act or a feat, making it all neat and easy
that naive theory can work with all the contents of logic because
it's a theory, and it's logic. There are plenty of interesting courses in it,
but I don't need a new model-theory for a proof-theory and don't need
homotopy type theory for class/set distinction and don't need Martin-Lof
type theory for type theory and don't need Dag's hypocritical commitments.




Now, to be fair, I should do something stupid to emulate Burse,
but nothing comes to mind.

[Mostowski Collapse]

Of course you need nothing, since you are a clueless moron.

[Ross Finlayson]

And your proof?

[Khong Dong]

On Thursday, 20 April 2023 at 16:40:04 UTC-6, Mitchell Smith wrote:
> On Monday, April 17, 2023 at 10:49:59 AM UTC-5, Khong Dong wrote:
> > On Wednesday, 12 April 2023 at 06:00:16 UTC-6, Mitchell Smith wrote:
> >
> > > Meanwhile, physicists have put themselves into a similar quandry. Like the computer scientists, they are blaming the evil mathematicians.
> > >
> > > The link cites some significant differences between Herbrand logic and first-order logic. By contrast, the Wikipedia page on a Herbrand structure conflates the two in its first sentence
> > >
> > > https://en.m.wikipedia.org/wiki/Herbrand_structure
> > >
> > > Again, this conflation is precisely why I put the first mention of "first-order logic" in scare quotes with the accompanying explanation.
> > >
> > > God may whisper into the ear of some people; but, he does not in mine.
> >
> > > When you all figure out how to use the word 'logic' unambiguously, I will do my best to accommodate the situation.
> > "Mathematics is the mortal introspection about own knowledge inference — via symbols in particular." -- https://qr.ae/prNPiu
> >
> > If you care/could, please "accommodate the situation". Thanks.
> >
> > > mitch

> Hi Nam. I hope you are doing well.

Hi Mitchell. I'm fine. Thanks. How are you doing? (It has been years!).

>
> What I believe about mathematics certainly involves our own mortality. I do not concern myself over infinities and circularities. Whatever may be the case with respect to their objective existence, they seem necessary to our explanations. For that reason, I associate them with our subjective experience.
>
> I do not believe mathematics to be a purely linguistic phenomenon. But, our capacity to reduce our representations to binary representations opens up the idea that the subjective experience of left and right is the fundamental experiential invariant upon which to understand "foundations."
>
> Our language is replete with dichotomies and binary oppositions.When we reduce mathematics to logic, we embark upon linguistic analyses. Russell had eventually written a paper asking if mathematics is purely linguistic. Logic certainly involves reductions based upon lingustic usage.

You might be interested in (especially Chapters 8, 10):

"General System Theory -- Foundations, Development, Applications"

https://monoskop.org/images/7/77/Von_Bertalanffy_Ludwig_General_System_Theory_1968.pdf

In particular:

<quote>

The Hopi "has no general notion or intuition of time as a smooth flowing continuurn in which everything in the universe proceeds at an equal rate, out of a future, through a present, into a past." (Whorf, 1952, p. 67).

Instead of our categories of space and time, Hopi rather distinguishes the "manifest," all that which is accessible to the senses, with no distinction between present and past, and the "unmanifest" comprising the future as well as what we call mental. Navaho (cf. Kluckhohn and Leighton, 1951) has little development of tenses; the emphasis is upon types of activity, and thus it distinguishes durative, perfective, usitative, repetitive, iterative, optative, semifactive, momentaneous, progressive, transitional, conative, etc., aspects of action. The difference can be defined that the first. concern of English (and Indo-European language in general) is time, of Hopi-validity, and of Navaho-type of activity (personal communication of Professor Kluckhohn).

Whorf asks:

How would a physics constructed along these lines work, with no t (time) in its equations? Perfectly, as far as I can see, though of course it would require different ideology and perhaps different mathematics. Of course, v (velocity) would have to go, too (1952, p. 7).

</quote>

"different mathematics", mind you!

[George Greene]

On Wednesday, April 12, 2023 at 8:00:16 AM UTC-4, Mitchell Smith wrote:
> This post is motivated by several recent conversations -- most notably,
> that with Mr. Burse in which I had been reminded of a prior conversation with Mr. Greene.
>
> Also, while I have not yet replied to Mr. Olson, he acquitted himself well
> with respect to the analytic conception of truth in reply to my remarks
> in the model theory thread. Naturally, I am not referring to the "correct reasoning"
> nonsense used to avoid acknowledgement that different paradigms must be respected.
> I did a quick Internet search on Herbrand logic to see if his use of metamathematical
> notation had any grounding in that logic.
>
> But, Herbrand logic is not based upon an analytical conception of truth.

You are *still* not an expert.

> One cannot make a case for his usage through that avenue.
>
> I did, however, find an informative web page from people working at Stanford University
> (Mr. Greene's alma mater). Among other things, it gives explicit differences between
> "first-order logic" and Herbrand logic.

Well, yes, they are different.
I sort of got that one very spectacularly wrong during the original argument, but
I think that argument *DID*FINALLY* end with my acknowledgment that I was originally
mistaken. At the time I was in a graduate program concentrating on "Herbrand models"
*FOR* the usual Tarskian semantics, so I was in the habit of intentionally obliterating
the relevant distinction.

> I placed the former in quotes because there are those who would
> simply define "logic" in terms of syntax alone.

You are over-claiming. You are STILL NOT an expert on "those" "other" people.
You have TO QUOTE THEM saying what THEY would do. In any case, the
dichotomy you are trying to draw here is obsolete -- if you START OUT by defining
logical consequence (and therefore "a logic") semantically IN TERMS OF MODELS,
then IT TURNS OUT that -- in the traditional first-order Tarskian case anyway --
THERE ALSO EXISTS A PURELY SYNTACTIC characterization OF THE SAME "logic",
of the same (semantically-defined) relation-of-logical-CONSEQUENCE.
It also turns out that for second-order logic, the (usual) semantic/model-theoretic
consequence-relation (under the "full" semantics) is so complex that any
traditional purely-syntactic characterization of it Is Too Hard (i.e. impossible
under the usual finitary constraints). Precisely for that reason, "alternative
semantics" for 2nd-order logic have gained some popularity, but (subjectively)
they are almost irrelevant precisely BECAUSE the tractability-gain that they
provide is fundamentally JUST DROPPING BACK DOWN TO *first*-order
logic (the Henkin semantics for 2nd-order logic is the canonical example of this).

[George Greene]

On Wednesday, April 12, 2023 at 9:42:00 PM UTC-4, Mitchell Smith wrote:
> I had been a database administrator during my information technology career.
>
> I taught myself. Read books on operating systems, Arcnet and TCP/IP networking, database systems, general purpose programming (C) and object-oriented programming (Eiffel), and Intel desktop hardware. I also taught myself Unix in an attempt to get a first job. Made it through 3 interviews with the team supervisor, but, the "team" rejected me in the last interview. To get experience, I volunteered with a not-for-profit taking care of their computers. I learned a proprietary desktop database called Dataflex.
>
> Dataflex had been the basis for actual employment in my first two jobs. I learned MS Access SQL at the second job as part of the product migration. With SQL, I landed a job at the National Center for Supercomputing Applications working with Sybase. That led to a job with IBM Global Services supporting nuclear power plants.Then I taught myself Oracle and foud a job with a local, regional university. I wrote an operational data store application acceppting IBM 360 mainframe data using Bourne shell, sed, and awk (who needs Perl? just more unnecessary make-a-buck technology). I never had the chance to convert it into a full-fledged C application.
>
> Because of a break forced on me because my mother went into hospice, I had some time and took corses with Sun Microsystems. I became a certified systems administrator and network administrator. My last "good" job had been as the quality assurance DBA for the Internet application division of the Bank of Montreal running Oracle test platforms on 26 Sun Microsystems servers.
>
> RDF had been proposed before the dot-com debacle. I had been studying all of the W3C technologies for the semantic web just before "math-believing" economists at the Federal Reserve trashed the US economy.

Are you talking about the crash of 2007-09?
That had a lot less to do with math and the federal reserve than it had to do with
deregulation of the securitized mortgage market. It was very much more political than
mathematical.


> Except, perhaps, when I have somtimes lost my temper,
> I have never been the person in this newsgroup dismissive of other people's mathematics.

You recovered very well professionally despite that.

> I find information technologies to be quite interesting.

I guess my problem was I did not. I never really had any interview where
demonstrating technical expertise *during* it was even required -- I had some
where somebody asked me a question and concluded from my answer that
I was ignorant, superficially. Sometimes disrespect gets palpably mutual.

[Ross Finlayson]

That reminds me of some cultures, where, expressing fear, invites violence, because,
it's an offense, to, take offense.

So, in these cultures it's better to have a real stoic conscientious bravery.

It's kind of like reverse discrimination, it's reverse discrimination, it's incrimination, ....
This is about the meaning of the word that to discriminate is the discriminant,
not the bigot. I don't like bigots making my language bigoted, that I need
wash my ears, though, in the interpersonal, I'm tender with words.

Wow I wonder how much peyote that new-age neo-Hopi cult asks you bring to orientation.
Also I don't want to know because I have no interest at all in their phone religion,
and am pretty sure that they have no contributions at all to my infraconsistency,
except as examples of sorts, of the lack thereof.

https://en.wikipedia.org/wiki/Dialectical_monism

The "dialectical monism" is a conscientious consciousness, common to all peoples.


I kind of prefer the color-blind approach, but not the blind approach.

One time we were watching a movie, it was black and white. I was like,
"damn, that guy sure is tan" and my, ..., friend was like "Ross, he's black".

I was kind of stunned for a second.

If there's a difference between black and African, it's that many black people are white.

And black, ..., for example mestizo, Asiatic, South Asiatic, Croats, Swedes, ...,
inner guys in a society with races.

Don't get me started on females, I already started on females a long time ago.
(Biology is innate, says my nuts, and with respect.)

I like to frame issues of race in terms of like "that man _has_ a black skin" instead
of that "that man _is_ a black man", not assigning identity, instead membership,
except positive things. "That man _has_ pronounced epicanthic folds", "that man
drives a low-rider", about, ..., "stereotypes". I leave people claiming identity to
the individual, then though that if they're not proud I don't want to know.

Don't get me wrong, there are bad examples of all sorts of people,
I'd rather not even know they exist.

About "tech" or computer programming, I've sat lots of interviews, and, I can't say
that I ever got a technical question that I didn't answer, and, that, at least half the time,
I arrived at alternate solutions, thus, they failed.

Indeed it would probably take a pretty creative person to get my drift.
I have it pretty easy though and fulfill usual work roles.

Now then about Herbrand, and Gentzen, no how about instead Kripke, and Sheffer,
keeping De Morgan, having a pi-calculus and theories of types all nicely, then for
systems of organization of "logical machines" or these "logical computing atoms"
for "geometrizations" that make for "the wind of truth", those can model Herbrand
and various relatively inconsistent models of Gentzen.

There's otherwise that "in silico" is "free-form, 3-D, I.C., standard and custom logic".

[Jeffrey Rubard]

Do you mean "Jacques Herbrand"?

[Mitchell Smith]

Hello George,

It is difficult for me to post inline.

You are correct, George --- I am not an expert. I came here around 2003 asking for help with axioms at which I had been looking. Instead, I had been flamed.

I owe you my gratitude. Your flaming forced me to educate myself. Yet, that education also made me aware of the fact that "mathematics" is largely divided into paradigms. Thus, while not an expert, I can make a reasonable argument for the defensibility of the first-order paradigm.

To your credit, you did acknowledge the difference as you have recalled.

With regard to "those others," there is a huge plurality if "logics" now. It is asking too much to address the many "purely syntactic" coneptions individually.

You are correct about the effect of soundness and completeness of first-order logic. One can ignore the semantic aspects because of the effective equivalence.

But, my work leads elsewhere.

Graham Cooper recently asserted that "mathematics is algebra." This is not so uncommon, and, one can certainly take Skolem's criticism of Zermelo as a major contribution in this direction.

But, as can be found in the 2022 FOM post by Tim Chow,

https://cs.nyu.edu/pipermail/fom/2022-June/023412.html

"It has long been known that certain results in complex geometry that have
a strongly algebraic flavor, and which you might think could be proved
algebraically, have so far been provable only via "transcendental" (i.e.,
analytic) methods. A remarkable byproduct of condensed mathematics is
that it yields new and much more algebraic proofs of many of these
results."


One cannot simply claim things like "mathematics is algebra," "mathematics is logic," or "mathematics is logic programming," when significant topics of mathematics cannot be subsumed within these kinds of claims.

In fact, the work to which Dr. Chow refers occurs in category theory with assumptions that would make ZFC consistent.

Anyway, you will be inclined to say, "But, this is sci.logic." My overlap simply comes from the fact that I began with an interest in the continuum hypothesis -- as a mathematical problem.

I hope all is well with you.

mitch

[Mitchell Smith]

I had lost my career in the dot-com fiasco.

Normally, the federal reserve would have slowed an economy like that of the 1990's. In particular, they knew that a jump in the economy had occurred in 1992 in response to a banking crisis with savings and loan institutions. As best that I can recall, they had intended to raise interest rates at that time.

But, they became aware of the Y2K issue. So, they tried to keep interest rates as low as possible so that large institutions could make the needed adjustments.

After January 1st of 2000, it had been either 19 or 21 interest rate hikes each successive month.

It destroyed all of the fledgling dot-com startups that were living off of borrowed money and put 250,000 information technology workers out of work. Human resource departments would request salary histories, and, no one would hire the previously better-compensated workers regardless of skills.

Then, of course, the 2001 attack in New York tanked the rest of the economic sectors.

Palpable mutual disrespect...

At one point before I knew Oracle, a Russian immigrant SASS programmer I had met at my first good job asked me to lie on my resume. He wanted me to join him at Abbott Labs. Naturally, I chose not to lie about my skills.

Later, I had been sitting in a job interview for a Sybase position. The recruiter knew nothing, but spoke at every opportunity about how the Russians were geniuses about databases. When I had become certain that I would not receive a job offer, I thought of my Russian colleague who wanted me on his team.

I told the recruiter I would be happy to accept the position at $125,000 per annum.

It seemed the best way to return the insult.

I miss those days. I was not an expert on computers, either. But, I was able to help people whose livelihood had become dependent on machines they did not understand.

mitch

[Mitchell Smith]

Thank you for this link, Nam.

Much of what I have looked at for the past hour is relevant to my views.

My original scientific interest had been biology. And, what I simply cannot comprehend is how a presumption of truth for the theory of evolution does not introduce an essential circularity into reductionist accounts of "science." If we are evolved biological organisms, then claims suggesting that we have a facility for discerning the truth of material reality carry a burden of proof not met by simply pointing to mathematics and physics.

So, there is the comparison with how one might have expected Kant to be awed with life, itself.

Obviously, people with different views see no burden of proof upon themselves.

And, I think a great deal about time different from an algebraic dimension.

It is certainly solipsistic to deny an objective reality simply because sensory experience would seem to impose limitations making objective reality contingent. If one insists, call this the solipsust's dilemma and resolve it with an assumption of an objective reality. The difficulty becomes one of reconciling experiential time with time as an algebraic dimension.


This has, more or less, translated into an interest in the aperiodic honeycomb of Kari and Culek,

https://www.semanticscholar.org/paper/An-Aperiodic-Set-of-Wang-Cubes-Cul%C3%ADk-Kari/0160bfae2af53a2f3df4f82aa0ab4b57ac331db8

I have not yet purchased this paper, or looked into the specifics of this paper through other sources But, the "numerology" is correct relative to finite geometries with which I work.

On a different note, your constructive standpoint might find rough sets more amenable,

https://en.m.wikipedia.org/wiki/Rough_set

They may be compared with the approximations using upper sums and lower sums from integration theory. I have not thought much about them for a very long time. But, string theory has a great many physics enthusiasts blaming mathematics for their woes. After discussions with an amatuer physicist with whom I correspond, I suggested that he look at rough sets. As might be expected, he liked it much better than the platonism he associates with ZFC.

mitch

[Mitchell Smith]

Pcunt,

I opened this thread to point out that you are clueless about any wider scope of logic or mathematics other than what you know from logic programming.

If I had any skill with graphic programs, I would caricature you in front of your computer with question marks over your head. The power cord would be running up into your lazy, fat ass.

The caption would read: "Shit for brains."

mitch

[Ross Finlayson]

If _ordinary_ or well-founded sets are in a universe of _extra-ordinary_ and recursive or
self-similar or with-an-infinite-descending-chain or otherwise not-inconsistent-multiplicities,
from an universal set on down, and ZFC is considered "Platonism", wouldn't that be considered,
"higher Platonism"?

Platonism is at least two things, and one of them is a defense of "mathematics independent
of the empirical or the rhetorical", another is "the ubiquitous success of mathematical models
in the empirical and all matters of mathematical science".

I don't think physics should reject "mathematical platonism" _at all_ and in fact it's un-scientific
to do so because of the universal success of mathematics, and indeed physics should _embrace_
mathematical platonism that "mathematics, the academic field" _owes_ physics a platonist's
mathematics that meets its needs of what it models as according to physical _interpretations_.

So if you imply "here have some broken mathematics now your physical theory isn't what's broken",
that's WRONG and un-scientific, non-conscientious, WRONG, and ERRONEOUS.

Anything physics' "theory of everything" needs a mathematics' "theory of everything".

That they're the same theory, is a usual "strong" platonism.

Now, reading into rough sets and about Lotfi Zadeh and the fuzzy, or "indeterminate",
modeling "indeterminacy", for example as the stochastic or "random", does not reflect
the causal in usual theories of physics, or at least _fundamental theories of all physics_,
where here nobody cares so much about application domains because it's all been done.

Here the "strong mathematical platonism" includes line-continuity, and field-continuity,
and signal-continuity, for Jordan measure and the usual curriculum and Dirichlet problem,
and has non-Cartesian functions for a countable continuous domain that's also a unique
central feature of mathematics called line-drawing and part of an entire "theory of everything",
at least, "geometrical".

[Mostowski Collapse]

Ok, I thought so, that nobody would pay you for
trolling, must come right from your screwed soul.

Thank you very much for your coming out.

LoL

[Mostowski Collapse]

What happened that you have become a complete asshole?
This incident, and other incidents:

Mitchell Smith schrieb am Freitag, 28. April 2023 um 00:36:12 UTC+2:
> I had lost my career in the dot-com fiasco.

> Then, of course, the 2001 attack in New York tanked the rest of the economic sectors.

> I told the recruiter I would be happy to accept the position at $125,000 per annum.

https://groups.google.com/g/sci.logic/c/wt-pacBrN1Q/m/GDJUaRsRBAAJ

Rule 1: Of usenet, never post biographic info.

Rule 2: Of usenet, if somebody posts biographic info,
its fake news designed to provoke some social engineering
on some other party. i.e. that some other party reveals biographic info.

Rule 3: Of usenet, if somebody does that, he could be never-
theless a payed troll, even if he shows you that he has a screwed soul,
could be a cover-up.

Anyway, enjoy your waste of time.

LMAO!

[Mostowski Collapse]

Still same conclusion and even one more:

Conclusion, Mitchell Smith is indeed a payed troll,
whereas Rossy Boy is just a clueless moron.

Neither of you can produce content for sci.logic
that has a certain sex appeal. The demotivators are:

Rule 4: Of usenet, if somebody posts math (physics a
platonist's mathematics bla bla) or FOM references
(Tim Chow bla bla) in sci.logic, he doesn't understand
the heritage and scope of mathematical logic.

Rule 5: Of usenet, if somebody posts math (physics a
platonist's mathematics bla bla) or FOM references
(Tim Chow bla bla) in sci.logic, he doesn't understand
the heritage and scope of mathematical logic.

[Mostowski Collapse]

FOM is full of lunatics:
http://timothychow.net/kalam-final.pdf

[Mostowski Collapse]

Lets say AOI is the axiom of infinity.

Is there some modal logic with:

|/- AOI
|- ~[]~AOI

I didn't try yet.

[Ross Finlayson]

If you happen to have it handy, would you mind posting all your rules?

[Ross Finlayson]

"The logic", Burse?:

(The "Bursae" is "German Students Union", a sort of cult-ish society.)

Anyways why I point out "logic is singular" is because it's what is, in effect,
de facto, so, thus, Burse's dissimulation of "private little worlds" where what he
thinks it says thinks it goes, or, "Burse's boxes: a place for each", is that,
underneath it all, Burse, if you actually keep opening the boxes,
soon you'll find, it really is: turtles, and, really, all the way down.

Of course that's a silly place, and there are universals, and, that's not it.

(Also it's very gruesome that sometimes a Burse's box has skeletons in it.)

So, Burse, what's in your box?

[Jeffrey Rubard]

Moronic "St. Pauli Girl"-isms for us? Wow, you must be old...
For the better sort: I believe the slogan would be something like *Stolz ohne Scholz*...

[Mostowski Collapse]

Were did you see me talk about "The logic" even remotely?
Are you mental or what? Every axiom systems adds new
rules to a logic, so that a new logic appers. Thats open ended.

Although some authors and the very idea of so called logical
axioms, implies the idea of a domain independent core.
But does such a domain indepedent core even exist.

This question is more fundamental than that of Logicism:

What is Neologicism?
https://mally.stanford.edu/Papers/neologicism2.pdf

Because we would still require that mathematics would
need to add some axioms. But you see again why your
nonsense is not sexy at all. It lacks some appeal,

because mathematics implies for logicians that you
talk about some domain, like the natural numbers, the
real numnbers, or some abstraction, like limits etc..

Whereas logicians prefer to look for domain indepent
logical axioms and inference rules. Thats probably something
where Rossy Boy and Mitchell Smith have a blind spot,

namely whats the topic of Logic? Whereas the topic
for a logician is always plural, Logics. You hardly
find a logician that wants to deal with "The Logic".

This happens more for people that believe in scientism.

Ross Finlayson schrieb am Freitag, 28. April 2023 um 17:29:32 UTC+2:
> If you happen to have it handy, would you

> mind posting all your rules? "The logic"

[Mostowski Collapse]

The rejection of "The Logic", doesn't mean
that there is no model theory or no proof theory.
You wouldn't condem a biologist that there is

no "The Nashorn" either? Or do you?

"In his essay Against Method he depicted the
process of contemporary scientific education
as a mild form of indoctrination, intended

for "making the history of science duller,
simpler, more uniform, more 'objective' and
more easily accessible to treatment by

strict and unchanging rules".
https://en.wikipedia.org/wiki/Against_Method

Rossy boy, are you also trying to make logic
as dull as possible? Your nonsense posts
don't make any sense at all!

Mostowski Collapse schrieb:

[Mostowski Collapse]

That there exists algebraic logic, doesn't change anything
that logicians don't want to do mathematics. They only
want to use mathematics. Understood! Possibly no, right?

That Mitchell Smith is a payed troll is then seen by nonsense such as:

Mitchell Smith schrieb am Sonntag, 9. April 2023 um 17:22:47 UTC+2:
"The algebraic picture is re-introduced into "foundations" when
Skolem points out that Zermelo's set theory cannot be categorical."
https://groups.google.com/g/sci.logic/c/pZZPoenTJoE/m/IDM-t3CaAwAJ

So basically sci.logic and sci.math got a new Rossy Boy,
only its a little bit more clever Rossy Boy. Posting gibberish
that is more difficult to decipher that the obvious

encyclopedic ChatGPT immitation by Rossy Boy.

Mitchell Smith schrieb:

[George Greene]

On Wednesday, April 12, 2023 at 8:00:16 AM UTC-4, Mitchell Smith wrote:
> But, Herbrand logic is not based upon an analytical conception of truth.

As usual, you do NOT know what THE FUCK you are talking about.
There IS NO SUCH THING as "Herbrand Logic".
Seriously, if you WOULD BOTHER TO GOOGLE IT, you would NOTICE that you
DO NOT GET ANY hits. Oh, you get pages where "Herbrand" and "logic" are both
mentioned, but when people SAY "Herbrand logic", what THEY -- since, UNlike you, THEY KNOW what they are talking about --
wind UP MEANING is first-order logic WITH HERBRAND *S*E*M*A*N*T*I*C*S. Herbrand's whole contribution here is based on
THE TERM MODEL.

> I did, however, find an informative web page from people working at Stanford University (Mr. Greene's alma mater).
> Among other things, it gives explicit differences between "first-order logic" and Herbrand logic.

NO IT DOESN'T. Good grief!
You cannot quote any of the explicit differences because you do not understand them.

> I placed the former in quotes because there are those who would simply define "logic" in terms of syntax alone.

NO THERE AREN'T. GOOD GRIEF!
Again, if you had ever studied any of this stuff, you would KNOW that THE COMPLETENESS THEOREM
OBLITERATES THIS DISTINCTION.

> Normaly, however, first-order logic is understood to have Tarski semantics.

Herbrand provided AN ALTERNATE SEMANTICS (an alternate candidate-method for model
construction)
>
> The web page is at the link,
>
>
>
> A passage within its conclusion had been of interest to me. It reads,
>
> "To test the value of Herbrand semantics in this regard,

Herbrand SEMANTICS, dipshit, NOT "Herbrand logic", which, I repeat, NObody talksqbout!


> we recently switched Stanford's introductory logic course from Tarskian semantics to Herbrand semantics.
> The results have been gratifying. Students get semantics right away. They do better on quizzes.

I don't know what to say to that. I had been introduced before I got there.
I had to take the introductory course there since it was computer-based and since
computer science and education were my two main fields of interest --
and at the non-introductory level, when I finally got around to taking the official
first-order logic course (OF COURSE with Tarskian semantics, although, since that
was the only alternative, we didn't know any different) I only got an A- instead of an A,
but it IS NOT like Herbrand semantics would have helped! Again, via the completeness theorem,
IT TURNS OUT YOU CAN DO FOL WITH SYNTAX *A*N*Y*W*A*Y*!

> And there are fewer complaints about feeling lost. It is clear that many
> students come away from the course feeling empowered and intent on using logic.
> More so than before anyway."
>
> Aww...
>
> Mathematics is hard. So, we should redefine mathematics so that people who are unwilling to put in the hard work can feel good about themselves.

Mitch,please, what degree did YOU finally finish???


> But, that is not what is going on here.
YOU WOULDN'T KNOW.

>
> Meanwhile, physicists have put themselves into a similar quandry. Like the computer scientists, they are blaming the evil mathematicians.
>
> The link cites some significant differences between Herbrand logic and first-order logic.

NO, IT DOESN'T. It talks about Herbrand MODELS, Herbrand BASES, and Herbrand STRUCTURES,
because the Herbrand variation is a variation IN SEMANTICS. Any change in the resultant logic
is a STRAIGHTFORWARD consequence of the change IN SEMANTICS, and people WHO KNOW
what they're talking about SAY "Herbrand semantics"or "Herbrand structures" or "Herbrand base"
AND NOT "Herbrand Logic".

By contrast, the Wikipedia page on a Herbrand structure conflates the two in its first sentence
>
> https://en.m.wikipedia.org/wiki/Herbrand_structure
>
> Again, this conflation is precisely why I put the first mention of "first-order logic" in scare quotes with the accompanying explanation.

Oh, shut THE FUCK up! The wikipedia page says Herbrand_structure because THAT'S A REAL THING.
"Herbrand logic" is YOUR fantasy. It's not a "conflation" if YOU can't cite them AS DIFFERENT!
And the link you gave at
http://intrologic.stanford.edu/extras/manifesto.html
DOES NOT make them different! IT CORRECTLY talks about Herbrand SEMANTICS
and about CHANGING TO that semantics!

[George Greene]

On Wednesday, April 12, 2023 at 8:00:16 AM UTC-4, Mitchell Smith wrote:

> The link cites some significant differences between Herbrand logic and first-order logic. By contrast, the Wikipedia page on a Herbrand structure conflates the two in its first sentence

>
> https://en.m.wikipedia.org/wiki/Herbrand_structure
>
> Again, this conflation is precisely why I put the first mention of "first-order logic" in scare quotes with the accompanying explanation.

There is no conflation going on. The fact that YOU want to define something differently does not make it different.
Definitions by definition are among a community of speakers. Advocating for change is one thing. Assuming that
you get to impose it by fiat (or worse accidentally, because YOU DIDN'T UNDERSTAND the prior definitions) is entirely another.

>
> God may whisper into the ear of some people; but, he does not in mine.
> When you all figure out how to use the word 'logic' unambiguously, I will do my best to accommodate the situation.

NO, YOU WON'T.
It's been decades and YOU STILL HAVEN'T.
That is not who you are. IN THE VERY LINK YOU QUOTED from Genesereth et al,
THEY are at pains to say "Relational Logic with the Herbrand semantics" AS OPPOSED TO "Herbrnad logic" --
UNlike you, THEY CLARIFY that the underlying system of inference can be thought of AS SAYING THE SAME
*WHILE* the semantics (the methodology for constructing models, and thence the models allowed) changes.

[Mostowski Collapse]

This is also a quite cool gem from La La land by our payed troll:

Mitchell Smith schrieb am Montag, 10. April 2023 um 04:16:36 UTC+2:
> Under Tarski's semantic theory of truth, it is possible for
reflexive equality statements to be false. That is something
else one will not find in a modern class on model theory.
And, it is why "foundational" claims reducing mathematics
to algebra fail to encompass analysis.
https://groups.google.com/g/sci.logic/c/pZZPoenTJoE/m/2EP4aR6-AwAJ

I dunno, if you use FOL and not FOL=, you can let
X = X fail. So what? Is this related to Tarskis T-Schema?
Probably not. Last time I saw Refl mentioned was in Agda:

Existentials, Universals, and Negation
; from∘to = λ{ ¬∃xy → extensionality λ{ ⟨ x , y ⟩ → refl } }
; to∘from = λ{ ∀¬xy → refl }
https://plfa.github.io/Quantifiers/#existentials-universals-and-negation

Some interesting identities where I guess the use
of "refl" makes explicit what is used in the identity as an
assumption to make it work. But FOL has also the

¬∃≃∀¬

So whats going on? Since these modern things like Coq
and Agda are polymorphic and higher order, what Refl
is even used? What does "open Eq using (_≡_; refl)" mean?

Does this imply that FOL has refl somewhere hidden?

[Mostowski Collapse]

Identity had indeed a kind of revival. If you want to
hear a couple of buzzwords, you might like Beck-Chevalley
condition etc.. Or six (Grothendieck’s) six operations.

What Herbrand semantics does to a model theoretic semantics
is tame. Concerning Refl, I like that Herbrand semantics
belongs to a "normalized" equality semantics where

/* Equality is the Domain Diagonal */
=_M = { (x,x) | x e D_M }

Which is not necessarely the case in some axiomatic approaches
to FOL=. But I forgot where this "normality" pays off? Also its
not the only characteristic of a Herbrand semantics.

To get into the Buzzwords try this:

Homotopy theoretic models of identity types
"This result indicates moreover that any model category has
an associated “internal language” which is itself a form of Martin-
L¨of type theory. This suggests applications both to type theory
and to homotopy theory.
Because Martin-L¨of type theory is, in one form or another, the
theoretical basis for many of the computer proof assistants
currently in use, such as Coq and Agda (cf. [2] and [4]), this
promise of applications is of a practical, as well as theoretical, nature."
https://arxiv.org/abs/0709.0248

[Ross Finlayson]

It's just plain type theory.

[Ross Finlayson]

That's just "algorithms and data structures". The objects of logic just like any
other objects or referents of reason all belong to "philosophy".

It's pretty much so for "theory", also.

Anyways your little data structures and their algorithms, for the calculi over them,
is a usual notion of a universal modality and a modal theory, a modal logic, all
one of them, unless you're a usual hypocritical sort who asks "what do you want
it to be".

Yeah, I know, at least one Burse troll, must emote a lol, or it's at best struck down
all "gibberish", its whole sad pathetic train-car of sock-puppet trolls.

It reminds me of "Lall", which is from this episode of old Star Trek. So anyways the
Enterprise finds some primordial-seeming planet and its people are this sort of
innocent noble savagery. Anyways between Chekov who's pretty much always at
fault and his ever-out-of-control hormones, and one of the hot lieutenants, they
dropped the Apple on Eden. So anyways this tribe was really a cargo cult basically
in the domain of Lall, which was sort of a mechanical robotic overlord, that fed on
their sacrifices and upon their gaining consciousness, tried to murder all the crew,
that only between sequestering the sacrifiants, and hitting its head with the phaser
array, it resulted that the savages entered a tribal adulthood, though I wonder that
it was really very much a violation of the Prime Directive.

It's kind of like "Landru", or "VGer", "I am NOMAD", usual enough caretakers of inmates,
tyrranical and cruel, concepts that Star Trek explored in the space-operatic or "science fiction".

Non sequitur, your logic is disorganized.


So anyways, what sort of "universal data structure" has "truth-values everywhere" and
so models "a universe of a space-time with all its contents"? It's usually called a theory,
a logics, and mathematics, a science, and a physics, and "the".

[Mostowski Collapse]

I guess even too vanilla for your Herpes infested brain.

[Mostowski Collapse]

Because his brain is a rottenness, sputum and pus mould
I guess the only "theory" that Rossy Boy can work out is:

0 = 0

But I wouldn't lean too much out of the window. Your
compatriot has already pointed out that it might fail.

Mitchell Smith schrieb am Montag, 10. April 2023 um 04:16:36 UTC+2:
> Under Tarski's semantic theory of truth, it is possible for
reflexive equality statements to be false. That is something
else one will not find in a modern class on model theory.
And, it is why "foundational" claims reducing mathematics
to algebra fail to encompass analysis.
https://groups.google.com/g/sci.logic/c/pZZPoenTJoE/m/2EP4aR6-AwAJ

[Ross Finlayson]

0 != 0

[Mostowski Collapse]

The misery with Rossy Boy is explained best here:

Nozick's "Philosophical Explanations"
https://antilogicalism.com/wp-content/uploads/2017/07/philosophical-explanations.pdf

Reading from Nozick's "Philosophical Explanations"
https://www.youtube.com/watch?v=6BNDx-FUwKM

Just take Nozick's "Let the relation E be the relation
correctly expalins or is the (or a) correct explanation of.
[...] The explanatory relation E is irreflexiv, ... [...]

Ha Ha, you sure. Ever heard of a Quine?

https://en.wikipedia.org/wiki/Quine_(computing)

[Mostowski Collapse]

Whats worse, Scientology or Technical Philosophy?
Both is a pile of shit, that even a fly wouldn't touch.

[Mostowski Collapse]

Holy cow! This is full of Σ-types. What do you think
about this approach to knowledge representation?

Formalizing Subsumption Relations in Ontologies using Type Classes in Coq
Richard Dapoigny1 Patrick Barlatier1
LISTIC/Polytech’Savoie University of Savoie, Annecy, (FRANCE)
https://www.irit.fr/TYPES2013/Slides/TYPES13Slides_Dapoigny_et_al.pdf

Is this a kind of new French Revolution,
to impute Coq to the world?

Mostowski Collapse schrieb am Mittwoch, 12. April 2023 um 16:42:19 UTC+2:
> What do you think about "Knowledge Graphs"?
>
> DeclarativeAI 2022 - Ivan Horcrux
> https://www.youtube.com/watch?v=hWBRO8s07sE
>
> Mitchell Smith schrieb am Mittwoch, 12. April 2023 um 14:00:16 UTC+2:
> > mitch

[Jeffrey Rubard]

On Monday, May 1, 2023 at 6:14:03 AM UTC-7, Mostowski Collapse wrote:
> Holy cow! This is full of Σ-types. What do you think
> about this approach to knowledge representation?
>

"The approach to knowledge representation is full of shit?"